So how do the e remain in orbit since gravitational force is negligible?
This is a very fundamental concept to organic and inorganic chemistry. The fact that you aren't clear on it means you need to go back to your textbook and read through sections on the quantum-mechanical picture of the atom.
In general, electrons in atoms do not have well-defined positions and momenta as one would expect classically - to do so would violate the Heisenberg uncertainty principle. Instead, we describe the state of the electron as being confined to an orbital, which is really a region in space where the probability of finding the electron is some constant, usually 90%. It turns out that, for a a single electron system, such as hydrogen, we can actually solve the Schrodinger equation which tells us what those probability functions would be and what energies they have associated with them. This gives rise to the familiar
s, p, d, and
f orbitals you've seen before.
For atoms with more than one electron, we can't actually solve the equation to get the probability functions because of, among other things, electron-electron repulsion. So, we make the approximation that the electrons don't interact at all and then use the probability functions we had for hydrogen. This allows us to, in some way, describe what's going on in atoms. The complete picture is actually quite a bit different and of course, the orbital picture changes considerably when we start talking about molecules and bonding.
For anyone reading this, understand that I've purposefully left out a lot of things and am being somewhat misleading about the probability functions. In reality, the solutions to the Schrodinger equation define the states of the electron, the so-called eigenvectors or stationary states of the electron, and the allowable energies for each state. The probability functions which are plotted in chemistry textbooks are usually the square of the wavefunction. None of this is all that important, but I wanted to be precise for posterity.
